Questions tagged [logic]

For questions about logic, whether it concerns syllogistic logic, mathematical logic or the nature of logic itself.

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The understanding of logic presuppose a kind of understanding of natural language,isn't it?

Our understanding of logic needs at least a basic understanding of words over a finite alphabet,natural language and numbers. For example,when we write down (one way) the definition of the atomic ...
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Is there an issue with the Socratic method arguing against points?

So, I've noticed something, looking at the classic example: Do the gods know everything? Yes. Do some gods disagree with others? Yes. So gods disagree about what is true? I ...
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Contradiction vs Inconsistency [closed]

Patrick Hurley. A Concise Introduction to Logic (2014 12 ed). pp 346-348. Can someone please distinguish contradictory vs. inconsistent statements more markedly and intuitively than the pages below? ...
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What is the difference between “logical equivalence” and “material equivalence”?

Wikipedia offers this as the difference between "logical equivalence" and "material equivalence": Logical equivalence is different from material equivalence. Formulas p and q are logically ...
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Does it hold that everything exists necessarily?

In Quantified modal logic, "constancy’s defenders can point to certain powerful arguments in its favor. Here’s a quick sketch of one such argument. First, the following seems to be a logical truth: ...
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If-then statements meaning in everyday vs mathematics

In mathematics when a "P implies Q" statement is true it means that every time P is true, Q is true also. What about everyday usage? For example consider the statement: "If it is raining, then I am ...
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Does the conditional statement “If not-p then p” have a name?

For there to be not-p it is necessary that there be p. It is easy to show that "If not-p then p" is true, and conversely "If p then not-p" is false. Further the contra-positive of "If not-p then p" ...
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“It is possible that this sentence is not true”

This is a "modal liar sentence" that I'm trying to use to illustrate how liar sentences are not well-formed. It seems like a nifty species to consider, and I never came across it before, but so... The ...
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Distinguishing arguments and explanations

For this question suppose that an argument is a rationale in which the reason presents evidence in support of a claim made in the conclusion, and an explanation is a rationale in which the reason ...
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Hypothetical Condition Leading a Result

To me the language in the following statement suggest a logical fallacy of some sort. I am not skilled in such matters, so I thought that someone in this forum might provide some insight. Thanks for ...
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What is the difference between a statement and a proposition?

I'm doing a MOOC on mathematical philosophy and the lecturer drew a distinction between a proposition and a statement. This is very puzzling to me. My background is in math and I regard those two ...
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What is the difference between intensional and extensional logic?

Homotopy type theory talks is conjectured to be the internal language of (infinity,1)-toposes; it comes in two flavours: extensional and intensional - these aren't notions that I've come across before ...
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Aristotelean obversion: not vs non-

Apr 30: Aristotelean contraposition consists of obverting an initial proposition, converting this obversion by switching the places of the first and second propositions (keeping any negation), and ...
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The Dratted Liar Again

Is there a formal or semantic difference between these sentences? This sentence is false. The sentence containing these words is false. EDIT: It seems the question is too ambiguous to be ...
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What is the difference between Law of Excluded Middle and Principle of Bivalence?

Law of Excluded Middle: In logic, the law of excluded middle (or the principle of excluded middle) is the third of the so-called three classic laws of thought. It states that for any ...
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Another logic proof problem I'm stuck on :(

sigh stuck on another problem Premises P Conclusion (( ~(Q → R) → ~P) → (~R → ~Q)) I am allowed to use Modus Ponens, Modus Tollens, Hypothetical Syllogism, Simplification, Conjunctions, Addition, ...
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Which fallacy: Thinking everything someone does in a discussion that's wrong is a fallacy?

There are a lot of questions about which fallacy something is on this site. Many times, the argument in the question is not actually a fallacy, but something that the questioner doesn't like/agree ...
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Why does “Daisy has four legs” not entail “Daisy has more than two legs”?

I have been going through one of the books and I found an example of conclusion C that is not entailed by a premise P. Daisy has four legs. So daisy has more than two legs. Surely though, the ...
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How do I complete the remainder of this quantified Fitch proof?

This is where I get stuck, how do I finish this proof? I only have access to intro and elif rules, not DS or anacon or others.
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Is double negation always applicable to commitments?

If I commit to X, am I always committing to not ~X? In classical propositional logic, double negation always the same as not negating at all. I'm curious if this principle applies to commitments. ...
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What is the difference between the resolution rule and the elimination in natural deduction?

I understand that elimination is: p v q ¬q then p and resolution is: q1 v q2 v q3...qn ¬q1 v q2 v q3...qn then q2 v q3...qn I see no difference, but my teacher is telling us don't use the ...
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Indirect Proof with contradiction in premises

The premises are as follow: 1. A 2. A > ~B 3. B 4. C The conclusion is (A & B) & \~C My teacher proceed to use solve it using Indirect Proof. 5. ~[(A & B) & ~C ] AP 6. ~B ...
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prove using natural deduction truth functional logic

can someone help me with my practice problems pls prove using natural deduction truth functional logic A → (B → C), D → B ∴ A → (D → C) 1 A → (B → C) 2 D → B 3 A 4 D 5 ...
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Can “A (logically) implies B” and “not-A (logically) implies B” be both true?

Suppose we have the following statements. They are logical implications. 1) A implies B. 2) Not A implies B. Can they both be true? I think no because if one of them is true then also its ...
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Where did Suárez say the principle of non-contradiction does not apply to the Trinity?

Fr. Réginald Garrigou-Lagrange, O.P., says, in Le Sens du Mystère et le Clair-Obscur Intellectuel: Nature et Surnaturel p. 128 fn. 1 (Engl. transl. p. 142 fn. 41): St. Thomas never would have ...
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What does it take to answer a philosophical question?

I apologize in advance if my question should be discussed on Philosophy Meta, but when thinking about the question I couldn't decide whether it would be appropriate there. Thinking about the ...
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What is a logical ground?

I've been stumbling upon the expression and am now asking myself what it's meaning is. What does mentioning a logical ground refer to? Perhaps anyone could try to break down the possibly multilayered ...
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Modal Logics Isomorphisms

What does it mean to say that the different branches of modal logic (temporal, epistemic, etc.) are isomorphic? I looked for the answer on The Stanford Encyclopedia of Philosophy, but couldn't find ...
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Fundamental Weakness in math?

Every proof in mathematics is an implication of the form A -> B where B is the proven statement and A is the premise (which can consist itself of many conjuncts like axioms, inference rules, theorems ...
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Semantic vs syntactic consequence

I see that the double turnstile ⊨ denotes the semantic consequence of some sentence of logic, and single turnstile ⊢ denotes the syntactic consequence of some model. This seems equivalent to me. Why ...
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Where is the Liar Paradox?

How would one go about proving that the Liar sentence is paradoxical? I ask because to me it obviously isn't one so I'd need a decent proof to change my mind. I've always been baffled as to why it's ...
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Is 'All sentences are false' false, true or paradoxical?

Usually you read that the sentence S: 'All sentences are false' is false because if true you got a contradiction, but if false it's not since it would just mean that not all sentences are false, e.g. ...
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What formal logical systems “resolve” the Liar Paradox?

Short version of my question. What formal logical systems can represent, and seem robust against, the Liar Paradox? N.B. I would like to avoid reference to truth-values, except inasmuch as they ...
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Do you believe that you should be able to get sociology deggree, no written test, you could just use Niccolò Makavelli, Plotinus, an Jesus, ect [closed]

Im really just trying to find out what some1 thinks is accurate an efficient according to the comparison of some critics, an or proffesionals. any ...
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Intuitionistic derivation of ~~~A --> ~A

I need to give an intuitionistic derivation of ~~~A --> ~A by using natural deduction. I know that in intuitionistic terms ~~~A --> ~A converts to ~~~A → ~A i.e ⊦ ((A → ⊥)→ ⊥→ ⊥) → (A → ⊥). These ...
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Distinguishing arguments from Nonarguments

Sometimes I cannot distinguish arguments from Nonarguments. For example, according to the book "A concise introduction to logic" by Hurley the following is an example of an argument: "There appears ...
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Non-consistent mathematical axioms

It is known that axioms are the building blocks of mathematics. Differents sets of axioms different "games". What I don't understand is how do we know that we pick axioms that are consistent? . Does ...
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Is RAA just MT?

If I say P and it leads to ~ Q then I have a false conditional . So imagine I want to prove ~ P then I show that Q is false as in If P then Q ~ Q ~ P We can do it the other way too If ~ P then ...
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Predicate Logic

How do I derive this? Pr 1 ∀x(Fx -> ∀xGx) ∴ ∀x(Fx -> ∀x(Gx \ / Hx)) My attempt: However I cannot used universal derivation due to the free x. I think using ass id and qn would be better ...
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Is there an intuitive justification of Peirce's Law?

I recently encountered Peirce's law, which states for a given proposition P, if there exists a proposition Q such that P follows from "if P then Q", then P is true. Alternatively: ((P→Q)→P)→P. Below, ...
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Is it possible for an argument to be logically valid but not truth-functionally valid?

Truth-functionally valid: there is no truth value assignment for which the premises (of an argument) are true yet the conclusion is false. I am told that there are arguments which are logically valid ...
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Post hoc fallacy Vs. Slippery slope fallacy

What are the differences between Post hoc fallacy and Slippery slope fallacy? Why they are different?
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Is it an informal fallacy to call an argument ridiculous without pointing out the flaw?

I think it is one kind of informal fallacy to dismiss a logical argument by just calling it ridiculous without actually showing how the argument is invalid. At first, I thought it to be ad hominem as ...
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Which fallacy was committed here?

In a discussion at the start of the COVID-19 outbreak there were people with the opinion that everyone was overreacting. I'm sorry but this is a massive over reaction in my opinion. Pneumonia kills ...
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Can we traverse an infinite?

Seems to me the problem of traversing an infinite is not a problem . Imagine if we start at place A . Do we get to B when place A and B are on an infinite line ? We get to B since the distance we move ...
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Can an omnipotent being create a world where 1+1=3?

This thought started off as 'If we are in a simulation, or if there exist a God/omnipotent being that can change the laws of physics (and everything) as we know it - is it possible for a change to ...
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Question on the “Property of an Object” and the “Action of an Object” (+the “State of an Object”)

I have confronted a philosophical problem related to the definition of the "property of an object." What I believe is: The capability of an object (the capability to desire) is the property of an ...
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Is fence sitting ever admirable and valuable?

This quote is from a website for an undergraduate law admissions test of 40 minutes: Don’t sit on the fence. Don’t say that each side in an argument has a point unless you go on to say which point ...
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The Concept of Trivialism

I understand trivialism is the position that everything is true, but I don't understand how it arrives there conceptually. The trivialist realizes that our natural (L)anguage (combined with our ...
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What is the ontological status of the laws of logic? [duplicate]

Are the laws of logic abstract objects that exist independently of physical things? Are they the same in all possible worlds? Are they man-made constructs, nothing more than ideas in our minds? Or ...

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